A note on second order Riesz transforms in 3-dimensional Lie groups

Fabrice Baudoin; Li Chen

doi:10.1007/s00013-021-01699-6

A note on second order Riesz transforms in 3-dimensional Lie groups

^*Corresponding author af dette arbejde

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

Abstract

We prove explicit L^p bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

Originalsprog	Engelsk
Tidsskrift	ARCHIV DER MATHEMATIK
Vol/bind	118
Nummer	3
Sider (fra-til)	291-304
Antal sider	14
ISSN	0003-889X
DOI	https://doi.org/10.1007/s00013-021-01699-6
Status	Udgivet - mar. 2022
Udgivet eksternt	Ja

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10.1007/s00013-021-01699-6

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abstract = "We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.",

keywords = "3- dimensional Lie groups, Elliptic Laplacian, Heisenberg groups, Martingale transform, Second order Riesz transforms, Sub-Laplacian",

author = "Fabrice Baudoin and Li Chen",

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AU - Chen, Li

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AB - We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

KW - 3- dimensional Lie groups

KW - Elliptic Laplacian

KW - Heisenberg groups

KW - Martingale transform

KW - Second order Riesz transforms

KW - Sub-Laplacian

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A note on second order Riesz transforms in 3-dimensional Lie groups

Abstract

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